Evaluate the following mathematical expressions involving decimals. What is the correct se… — Armed Services Vocational Aptitude Battery (ASVAB)

Evaluate the following mathematical expressions involving decimals. What is the correct sequence of these expressions when ordered from least to greatest value?

1 $0.15 \times 40 - 14.4 \div 1.2$
2 $10.5 - 3.2 \times 2.5$
3 $(4.2 - 1.8) \div 0.6 + 0.5$
4 $2.4 \times 0.5 + 1.8 \div 0.3$

Answer

The correct order from least to greatest is:

0.15 \times 40 - 14.4 \div 1.2

, followed by

10.5 - 3.2 \times 2.5

, then

(4.2 - 1.8) \div 0.6 + 0.5

, and finally

2.4 \times 0.5 + 1.8 \div 0.3

Evaluating each expression using the correct order of operations yields final decimal values of

7.2

2.5

-6.0

, and

4.5

. Arranging these values numerically from least to greatest provides the correct structural sequence.

Step-by-Step Solution

Evaluate the first expression:

2.4 \times 0.5 + 1.8 \div 0.3

1.2 + 6 = 7.2

According to the order of operations, multiplication and division are performed left-to-right before addition.

Evaluate the second expression:

10.5 - 3.2 \times 2.5

10.5 - 8.0 = 2.5

Multiplication must be performed before subtraction.

Evaluate the third expression:

0.15 \times 40 - 14.4 \div 1.2

6.0 - 12 = -6.0

Perform multiplication and division first. Then subtract the larger value from the smaller value, resulting in a negative number.

Evaluate the fourth expression:

(4.2 - 1.8) \div 0.6 + 0.5

2.4 \div 0.6 + 0.5 = 4 + 0.5 = 4.5

Operations inside parentheses take highest priority, followed by division, and finally addition.

Order the evaluated results from least to greatest.

-6.0 < 2.5 < 4.5 < 7.2

Arranging the numerical values based on their algebraic magnitude provides the final sequence.

Key Concept

Order of Operations with Decimals

Alternative Method

Convert all terminating decimals to fractions (e.g.,

0.5 = \frac{1}{2}

0.3 = \frac{3}{10}

) before performing the operations to avoid decimal placement and alignment errors.

Estimated Time:1m 30s

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Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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